Can someone please explain why sin2x = sqrt 2/2 has angles of pi/4, 3pi/4, 9pi/4, 11pi/4? I don't understand where the 9pi and 11 pi are coming from.

Question

campbell_st · Answer

well there seems to be a slight mistake 

if 

$$\sin(2x) = \frac{\sqrt{2}}{2} ~~~~then~~~~~ 2x = \frac{\pi}{4}~~~or~~~ x = \frac{\pi}{8}$$

anonymous · Answer

what if I gave you a different example?

campbell_st · Answer

but basically its because the curve repeats... based on the information it repeats over a distance of pi.... so the period is pi.. 


draw the cruve 

draw a horizontal line through y = srt(2)/2 and you'll see how many times the horizonal line intersects sin(2x) 

and it forms a pattern....

a rough sketch is shown below


|dw:1414350994222:dw|

hope it helps